Thousands of Turkish troops have crossed into northern Iraq in their hunt for Kurdish PKK guerrillas, a senior military source said on Friday, in an escalation of a conflict that could destabilize the region.

Turkey's military said the land offensive had fighter aircraft in support. Turkish TV said 3,000 to 10,000 soldiers had entered Iraq, though Iraq's foreign minister denied it was a major operation, saying only a few hundred troops were involved.

The European Union repeated its call for Turkey, which is seeking EU membership, to refrain from any disproportionate military action. Britain urged Ankara to leave Iraqi territory as early as possible and Washington also raised concerns.

The Turkish Armed Forces, which attach great importance to Iraq's territorial integrity and stability, will return home in the shortest time possible after its goals have been achieved, the General Staff said in a statement posted on its Web site.

The military source based in southeast Turkey told Reuters: Thousands of troops have crossed the border and thousands more are waiting at the border to join them if necessary.

A PKK spokesman in northern Iraq said rebels were battling the Turkish troops.

There are severe clashes. Two Turkish soldiers have been killed and eight wounded. There are no PKK casualties, Ahmed Danees, head of foreign relations for the PKK, told Reuters by satellite phone from an undisclosed location.

It was not possible to independently verify his statement.

Iraq's foreign minister played down the operation.

There has not been any major incursion or land invasion ... What is going on is around a few hundred Turkish forces have crossed the border looking for the PKK or their bases, Hoshiyar Zebari told Reuters by telephone.

The U.S. military said it was aware that Turkish forces had launched the offensive against the Kurdistan Workers Party (PKK), considered a terrorist group by Ankara, the United States and the European Union.

Rear Admiral Gregory Smith, a U.S. military spokesman in Baghdad, said the operation was understood to be of limited duration and aimed solely at PKK fighters hiding in the area.

NATO member Turkey says it has the right under international law to hit Turkish PKK rebels who shelter in northern Iraq and have mounted attacks inside Turkey that have killed scores of troops. Turkey says some 3,000 PKK rebels are based in Iraq.

Ankara blames the PKK for the deaths of nearly 40,000 people since it began an armed struggle for a Kurdish homeland in southeast Turkey in 1984.

HELICOPTERS, TANKS

Turkey's military said the cross-border offensive was launched at 7 p.m. (12 p.m. EST) on Thursday.

Turkish television said troops, backed by warplanes and Cobra attack helicopters, had moved 25 km (16 miles) inside Iraq. Television footage showed dozens of tanks moving at high speed near the Iraqi-Turkish border.

Turkish financial markets weakened on news of the offensive. Turkish opposition politicians applauded the decision to go in.

But a senior U.S. State Department official said the land incursion was not the greatest news.

A land operation is a whole new level, Deputy Assistant Secretary of State Matthew Bryza told reporters in Brussels.

He said Washington had been cooperating fully with ally Turkey in providing intelligence on PKK positions in northern Iraq since last November to enable the Turkish air force to make pinpoint attacks minimizing civilian casualties.

The EU and the United States have in the past raised concerns that a major offensive could destabilize the region, though they have not criticized recent small cross-border raids.

We understand the concerns of Turkey ... but we think this action is not the best response. The territorial integrity of Iraq is for us very important, EU foreign policy chief Javier Solana told a news conference in Slovenia.

Analysts said a potential flash point would be if Iraq's Kurdish Peshmerga security forces were to clash with Turkish troops. Turkey has accused the Peshmerga of sheltering the PKK.

Turkish President Abdullah Gul said he had called Iraqi President Jalal Talabani, a Kurd, to inform him of the incursion after it began.

Iraq's central government, which has little sway over Kurdish northern Iraq, has repeatedly called for a diplomatic solution to the PKK problem but Turkey's government is under domestic pressure to take military action against the rebels.

Turkey launched several major land offensives in the 1990s into northern Iraq against the PKK, but failed to dislodge them.

Militarily, even 50,000 troops in the 1990s were not able to destroy the PKK, but psychologically this operation could be quite effective. It has taken the PKK by surprise, said Gareth Jenkins, an Istanbul-based expert on Turkish security issues.

Because of the winter weather conditions, a land operation of this size will be very difficult.

Turkey's military said the PKK was the target of the ground offensive and vowed to act with restraint towards local groups.

(Additional reporting by Michael Holden and Mariam Karouny in Baghdad, Paul Taylor in Brussels, Mark John in Brdo, Selcuk Gokoluk and Gareth Jones in Ankara; Editing by Tim Pearce)